#/***********************************************************
#    cfint.rb -- 連分数補間
#***********************************************************/
N = 5             # 点の数 
x = []; y = []    # N 個の点の x 座標, y 座標 


def maketable(x, y)  # 係数を求め y[] に上書き 
    for j in 0...N
        for i in (j+1)...N
            y[i] = (x[i] - x[j]) / (y[i] - y[j]).to_f
        end
    end
end

def interpolate(t, x, y)  # 補間 
    r = y[N - 1]
    (N - 2).downto(0) {|i| r = (t - x[i]) / r.to_f + y[i]}
    return r
end

PI = 3.14159265358979323846264

for i in 0...N
    x[i] = 20 * i;  y[i] = Math::tan(x[i] * PI / 180)
end
maketable(x, y)
0.step(80, 2) do |i|      # 補間 
    s = interpolate(i, x, y)
    printf("%2d  % .14f  % .2e\n",\
        i, s, s - Math::tan(i * PI / 180))
end

exit 0